Existence and multiplicity of solutions for the noncoercive
Neumann p-Laplacian

Nikolaos S. Papageorgiou, Eugenio M. Rocha
Abstract:
We consider a nonlinear Neumann problem driven by the p-Laplacian
differential operator with a nonsmooth potential
(hemivariational inequality). Using variational techniques
based on the smooth critical point theory and the second
deformation theorem, we prove an existence theorem and a
multiplicity theorem, under hypothesis that in general do not
imply the coercivity of the Euler functional.